About Combinations
A combination is a selection of items (sample) from a collection, such that the order of selection does not matter.
A combination with reposition (or repetition) is a combination where each item may be selected any number of times.
For example, given four letters: A, B, C and D there are 10 combinations with reposition of two that can be drawn from this collection:
- A and A
- A and B
- A and C
- A and D
- B and B
- B and C
- B and D
- C and C
- C and D
- D and D
Thus, the number of possible combinations with repetition of 2 samples from a 4 item collection is 10.
Unlike permutations, combinations consider the order of the sample not relevant.
Combinations Formula
The formula for combinations with reposition is:
C(n,k) = (n+k-1)! / [ k! (n-1)! ]
Where n is the collection size and k is the sample size.
Combinations with Repetition Example
A bag has 6 balls of different colors. Each time a ball is drawn it is put back in the bag. 5 balls are drawn (with reposition). How many possible outcomes exist ?
C(50,5) = (6 + 5 - 1)! / [ 5! (6 - 1)! ] = 252
For more info on Combinations: https://en.wikipedia.org/wiki/Combination